Robust LPV Control for Attitude Stabilization of a Quadrotor Helicopter under Input Saturations

This article investigates the robust stabilization of the rotational subsystem of a quadrotor against external inputs (disturbances, noises, and parametric uncertainties) by the LFT-based LPV technique. By establishing the LPV attitude model, the LPV robust controller is designed for the system. The weighting functions are computed by Cuckoo Search, a meta-heuristic optimization algorithm. Besides, the input saturations are also taken into account through the Anti-Windup compensation technique. Simulation results show the robustness of the closed-loop system against disturbances, measurement noises, and the parametric uncertainties

A novel robust disturbance rejection anti-windup framework

This is an Author's Original Manuscript of an article submitted for consideration in the International Journal of Control [copyright Taylor & Francis] and is available online at http://www.tandfonline.com/10.1080/00207179.2010.542774In this article, we propose a novel anti-windup (AW) framework for coping with input saturation in the disturbance rejection problem of stable plant systems. This framework is based on the one developed by Weston and Postlethwaite (W&P) (Weston, P.F., and Postlethwaite, I. (2000), ‘Linear Conditioning for Systems Containing Saturating Actuators’, Automatica, 36, 1347–1354). The new AW-design improves the disturbance rejection performance over the design framework usually suggested for the coprime-factorisation based W&P-approach. Performance improvement is achieved by explicitly incorporating a transfer function, which represents the effect of the disturbance on the nonlinear loop, into the AW compensator synthesis. An extra degree of freedom is exploited for the coprime factorisation, resulting in an implicitly computed multivariable algebraic loop for the AW-implementation. Suggestions are made to overcome the algebraic loop problem via explicit computation. Furthermore, paralleling the results of former work (Turner, M.C., Herrmann, G., and Postlethwaite, I. (2007), ‘Incorporating Robustness Requirements into Antiwindup Design’, IEEE Transactions on Automatic Control, 52, 1842–1855), the additive plant uncertainty is incorporated into the AW compensator synthesis, by using a novel augmentation for the disturbance rejection problem. In this new framework, it is shown that the internal model control (IMC) scheme is optimally robust, as was the case in Turner, Herrmann, and Postlethwaite (2007) and Zheng and Morari (Zheng, A., and Morari, M. (1994), ‘Anti-windup using Internal Model Control’, International Journal of Control, 60, 1015–1024). The new AW approach is applied to the control of dynamically substructured systems (DSS) subject to external excitation signals and actuator limits. The benefit of this approach is demonstrated in the simulations for a small-scale building mass damper DSS and a quasi-motorcycle DSS

Incorporation of Robustness Properties into the Observer Based Anti-Windup Scheme in the Case of Actuator Uncertainties

Abstract-Saturation is a very common nonlinearity in control systems and may produce serious performance deterioration or even loss of stability. To cope with saturation, several anti-windup (AW) schemes have been developed over a long time. Unfortunately, they are based on the assumption that there is a static nonlinearity between the output of the controller and the plant input, which, in many situations, is not the case, because of an actuator dynamics. Against this background we provide a design procedure for the design of the AW-compensator that guarantee stability of the observer based anti-windup to face unmodeled actuator dynamics and guarantee a certain level of performance. This mixed performance method is later extended for systems with unmeasurable actuator outputs by the use of an unknown input observer (UIO). The effectiveness of the presented algorithm is demonstrated on an engine test-bench simulator. I. INTRODUCTION S result of physical limitations, the output of actuators is always limited in amplitude and rate, such as maximum or minimum torque in an engine or the maximum safe pitch rate in an aircraft. Such limits must be taken in account in the control design, otherwise the controller output will be different from the plant input, leading to wrong update of the controller states and to consequences ranging from performance deterioration over large overshoots and sometimes even to limit cycles or stability loss. Therefore, this phenomenon -usually called "controller windup" -has a paramount practical relevance and therefore many existing techniques address this problem of actuator constraints, e.g. the "Model Predictive Control" (MPC) Among the many contributions to handle input constraints for this class of problems, we recall the recent surveys of Galeani [3], Tarbouriech and Turner [4] about early and recent anti-windup research. The observer-based antiwindup design goes back to the publications of Åström and Hägglund Martin Bruckner and Luigi del Re are with the Institute for Design and Control of Mechatronical Systems (e-mail: [email protected]; [email protected]). In the case of actuator or plant uncertainties there are only a few contributions, such as the approach of Teel In this paper based on the Integral-Quadratic-Constraints (IQCs) framework we extend the observer-based antiwindup design procedure to handle actuator uncertainties and present a design procedure that allows tuning the AW for performance requirements. To this end two weighting matrices are introduced in the performance criteria. In addition some nicely interpretable rules are provided for choosing the weighting matrices. In the case, where the true plant input can't be measured the closed-loop system is extended with an unknown input observer (UIO). To the best of our knowledge, we are not aware of any work in the literature dealing with a mixed performance AW-design, jointly tackling both, unmeasurable actuator outputs and dynamic actuator uncertainty. All these algorithms are tested on an engine test-bench simulation example. The paper is structured as follows: first we introduce the observer based anti-windup compensator and present some robust stability considerations in the case of actuator uncertainties based on the IQC-framework. Afterwards an UIO is introduced to keep the performance in the case, when the output of the actuator isn't available for measurement. Finally the method is tested on a test-bench simulator. II. OBSERVER BASED ANTI-WINDUP DESIGN For reasons of global stability, throughout the paper the plant P of order n is assumed to be stable, and that the controller ( , , , ) c c c c A B C D stabilizes the system when the saturation is not active. The plant is described by the standard equations: is the state-space realization of the controller and L is the desired feedback matrix of the antiwindup compensator (se

Incorporating robustness requirements into antiwindup design

This paper treats the problem of synthesizing antiwindup compensators that are able to handle plant uncertainty in addition to controller saturation. The uncertainty considered is of the frequency-weighted additive type, often encountered in linear robust control theory, and representative of a wide variety of uncertainty encountered in practice. The main results show how existing linear matrix inequality based antiwindup synthesis algorithms can be modified to produce compensators that accommodate uncertainty better. Embedded within these results is the ever-present performance - robustness tradeoff. A remarkable feature is that the often criticized internal model control antiwindup solution emerges as an ldquooptimally robustrdquo solution. A simple example demonstrates the effectiveness of the modified algorithms

Incorporating robustness requirements into antiwindup design

This paper treats the problem of synthesizing antiwindup compensators that are able to handle plant uncertainty in addition to controller saturation. The uncertainty considered is of the frequency-weighted additive type, often encountered in linear robust control theory, and representative of a wide variety of uncertainty encountered in practice. The main results show how existing linear matrix inequality based antiwindup synthesis algorithms can be modified to produce compensators that accommodate uncertainty better. Embedded within these results is the ever-present performance - robustness tradeoff. A remarkable feature is that the often criticized internal model control antiwindup solution emerges as an ldquooptimally robustrdquo solution. A simple example demonstrates the effectiveness of the modified algorithms